integrator

This method is used to define an integrator. In the context of dynamic analysis, the integrator implements a time-stepping algorithm for ordinary differential equations. In the context of static analysis, the integrator implements a numerical continuation method. More specifically, the integrator performs the following:

1. determine the predictive step for time \(t+\Delta t\), \(\Delta \boldsymbol{u}\) in static analysis, \(\Delta \boldsymbol{u}\), \(\Delta \dot{\boldsymbol{u}}\), and \(\Delta \ddot{\boldsymbol{u}}\) in a transient analysis.

2. specify the residual and tangent at any iteration, i.e. what constitutes the \(\boldsymbol{A}\) matrix and \(\boldsymbol{b}\) vector in \(Ax=b\).

3. determine the corrective step based on the x vector, i.e. given \(x\) what is \(\Delta \boldsymbol{u}\) in Static analysis, \(\Delta \boldsymbol{u}\), \(\Delta \dot{\boldsymbol{u}}\), and \(\Delta \ddot{\boldsymbol{u}}\) in a transient analysis.

pythontcl

Model.integrator(type, *args)

Set the integrator type to be used by the Model.

Parameters:

• type (string) – The integrator type.

• args – A list of arguments for that type.

The type of integrator used in the analysis is dependent on whether it is a static analysis or transient analysis.

Static Integrators

• LoadControl
• DisplacementControl
• MinUnbalDispNorm
• Arc-Length Control

Transient Integrators

• Central Difference
• Newmark
• Hilber-Hughes-Taylor
• Generalized Alpha Method
• TRBDF2
• Explicit Difference

References

• Clarke, M.J. and Hancock, G.J. (1990) ‘A study of incremental‐iterative strategies for non‐linear analyses’, International Journal for Numerical Methods in Engineering, 29(7), pp. 1365–1391. Available at: https://doi.org/10.1002/nme.1620290702 .

Code developed by: fmk